Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library: kalman
See also: rICfil calibrIC

Quantlet: ICerzsep
Description: Auxiliary routine for rICfil: - if possible - generates for Lambda=Lambda1+Lambda2, Lambda1~N(0,S1), Lambda2~N(0,S2) indep a Hampel-Krasker-IC psi to efficiency loss e, i.e. E psi Lambda' = EM, E psi=0 (1) E |psi|^2= (1+e) tr ((S1+S2)^{-1}) and psi= A (Lambda1 w_b + Lambda2) w_b=min(1,b/|A Lambda1|) For dim p==1 a Newton-Algo is used for both a and b, for dim p>=2 for A a fixed-point-algorithm and for b a "careful" bisection method is used. Integration for A and p==2 is done by a Romberg-procedure. Integration for A and p>2 is done by a MC-procedure.

Usage: {A,b,V,ctrl}=ICerzsep(e,S1,S2,A0,b0,N,eps,itmax,expl,fact0,aus)
Input:
e numeric; efficiency loss to attain
S1 p x p; Covariance of the first (clipped) component
S2 p x p; Covariance of the second (unclipped) component
A0 p x p; starting value for A; if 0 is entered I^{-1} is taken else if p>1 and dim(A0)==1 FI^{-1}*A0 is taken and if p==1 and A0<0 , -A0/FI is taken
b0 numeric; starting value for clipping height; if 0 is entered 4*max(vec(abs("A0"))) [i.e. perhaps modified]
N integer; MC-sample size / integration grid-points
eps numeric; exactitude
itmax integer; maximal number of ICerzseptions
expl numeric; threshold for the changes in abs. value of A: beyond this value convergence is uncertain ~ 4
fact0 numeric (>1)!; factor determining how fast we descend from b to b
aus integer; 0: no output during execution, 1: some output, 2: more output, 3: a lot of output
Output:
A p x p; Lagrange-Multiplyer solving (1)
b 1; clipping height
V p x p; corresponding Covariance
ctrl integer; tells if convergence "happened"

Note:

Example:
to be looked up in rICfil

Result:
n/a



Author: P. Ruckdeschel, 19991010
(C) MD*TECH Method and Data Technologies, 05.02.2006